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Global testing for dependent Bernoullis

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Suppose $(X_1,\ldots,X_n)$ are independent Bernoulli random variables with $\mathbb{E}(X_i)= p_i$, and we want to test the global null hypothesis that $p_i=\frac{1}{2}$ for all $i$, versus the alternative that there is a sparse set of size $s$ on which $p_i\ge \frac{1}{2}+A$. The detection boundary of this test in terms of $(s,A)$ is well understood, both in the case when the signal is arbitrary, and when the signal is present in a segment.

We study the above questions when the Bernoullis are dependent, and the dependence is modeled by a graphical model (Ising model). In this case, contrary to what typically happens, dependence can allow detection of smaller signals than the independent case. This phenomenon happens over a wide range of graphs, for both arbitrary signals and segment signals.

This talk is based on joint work with Nabarun Deb, Rajarshi Mukherjee, and Ming Yuan

This talk is part of the Statistics series.

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